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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

The set (A B C) (A B ^ ′ C ^ ′ ) ^ ′ C is equal to

The set (A∪B∪C)∩(A∩B′∩C′)′∩C\left(A \cup B \cup C\right) \cap {\left(A \cap {B}^{′} \cap {C}^{′}\right)}^{′} \cap C is equal to

Options

  1. AA∩BA \cap B
  2. BAA
  3. CB∩C′B \cap {C}^{′}
  4. DCC

Correct answer

D. CC

Step-by-step solution

(A∪B∪C)∩(A∩B′∩C′)′∩C\left(A \cup B \cup C\right) \cap {\left(A \cap {B}^{′} \cap {C}^{′}\right)}^{′} \cap C
=(A∪B∪C)∩(A′∪B∪C)∩C= \left(A \cup B \cup C\right) \cap \left({A}^{′} \cup B \cup C\right) \cap C
=[(A∩A′)∪(B∪C)]∩C= \left[\left(A \cap {A}^{′}\right) \cup \left(B \cup C\right)\right] \cap C
=(ϕ∪B∪C)∩C=(B∪C)∩C=C= \left(ϕ \cup B \cup C\right) \cap C = \left(B \cup C\right) \cap C = C
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